Month: August 2016

BEDMAS 101

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It has always been a pet peeve for me when there are people around me who still do not know the BEDMAS rule. But then I always think this over the moment I hear that someone beside me in the library would argue with all their might to their friend that that 2 + 8 x 3 is 30 and not 26. But hey, I would then understand that Math is a tricky subject and that anything Math-related especially these types of problems can be quite confusing. Nevertheless, rather than being mad at that guy over at the library, it would be better if I teach them the ways of the BEDMAS.

Now BEDMAS, which stands for Brackets, Exponents, Division/Multiplication and Addition/Subtraction, represents the order of operations. It is a very handy mnemonic to easily remember the precedence among operations. There are other names for BEDMAS and one in particular would be PEMDAS, which is Parentheses, Exponents, Multiplication/Division and Addition/Subtraction. Both work the same way, as long as the order of operations is still followed.

So how does this work? The rule states that any operation found within brackets or parentheses must be worked out first. It is also important to note that the innermost grouping symbol has to be operated first before the outermost grouping. For instance, in calculating 3 x [2 – (4 + 5)], we solve first for 4 + 5 to get 9. Replace the  (4 + 5) in the original expression as 9 to make the expression much simpler by reducing the number of grouping symbols. So we then have 3 x [2 – 9]. Solving the operation inside the brackets which is 2 – 9 = -7. Replace [2 – 9] with -7, which leaves us with 3 x -7 and therefore can easily be solved to get -21.

The next precedence would be Exponents. After getting rid of the grouping brackets, then it is time to attack exponents. For instance, calculate 40 / (6 – 2^2)^3. Note here that “/” means division and “^” means an exponent raised to the power of. So here we start solving for the bracket which is 6 – 2^2. Here we see an exponent, which we should solve first. 2^2 is 4 and it should replace 2^2 here. Therefore 6 – 4 = 2. This was initially part of the bracket in the original expression and we should replace this with the number we got which is 2. Our simplified expression would thn be 40 / 2^3. Now recall that Exponents must go before any Multiplication, Division, Addition or Subtraction. Therefore 2^3, which is also equal to 2 x 2 x 2, is 8. Replace 2^3 with 8 to get 40 / 8, which is 5.

Now always keep mind to solve for bracketed operations first, beginning from the innermost operation to the outermost. Then any exponents found must be solved immediately before solving for any operation with Division, Multiplication, Addition or Subtraction. Division and Multiplication have interchangeable precedences, meaning that the first operation that appears after reading the expression from left to right has to be performed first. A simple example, for instance, would be 6 / 3 x 2. Here we first operate 6 / 3 to get 2 before multiplying it to 2 to get 4. If we have 3 x 9 / 27, therefore we first solve 3 x 9 before dividing the result by 27, which is equal to 1. Addition and subtraction, however have lower precedences than Division and multiplication; thus, division and multiplication would have to be performed first before operating addition and subtraction, while of course keeping the interchangeable precedence premise among division and multiplication. Moreover, like division and multiplication, addition and subtraction also have interchangeable precedences, performing first the operation that appears when the expression is read from left to right.

Here’s a recap of the rules of BEDMAS:

  1. Begin performing bracketed operations in an expression, starting from the innermost going to the outermost brackets (or parentheses or braces or any other grouping symbol for that matter).
  2. Simplify exponents whenever possible.
  3. Solve for division and multiplication operations. Precedences are interchangeable.
  4. Finish up with addition and subtraction. Precedences are also interchangeable.
  5. Repeat back to step 1 if there are any other further brackets and continue performing the cycle.

Now go and test yourself if you can calculate the final result of the following expressions using BEDMAS rule, and then check your answers:

  1. (2^7 – 1 x 5) + 3^4
  2. 1 + 1 + 1 + 1 + 1 x 0
  3. 180 / [2 + (8 x 1/2)]^2

Answers:

  1. 214
  2. 4
  3. 5

– Royalle
Date of Post: 08.20.16

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A Dream Map

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One of the things that got me fascinated about here in Toronto are bus and subway map routes. It’s never a surprise that I could navigate my way from one spot to the next by just riding and hopping through buses and trains. That’s why my friends here always count on me to be the “navigator” whenever we go on our “little adventures”.

As I was saying, my fascination for these things has led me to come to get to know the bus routes and subway station names much easier especially when I am in a foreign place. For instance, last summer my family and I went for a little vacation to New York and one knows how complex subway lines are there upon first glance. But trust me, once you get to know it, you can easily navigate where you are and where you are headed to, not to mention which subway lines to ride and what not.

Just recently last week, I finished building up my own subway dream map for Toronto. I included in the map the current existing one, while extending some subway lines and adding some new ones, with their corresponding subway stations. I would think that it would be great if Toronto would get rid of all its buses and focus on building more subways instead.

Environment-friendly? Well, not necessarily. The construction of a subway station and trains can sometimes be considered factors for the destruction of our environment, and can be very costly too when it comes to expenses. But hey, these are just some of my opinions. Tell me what you think about it, as well as the subway dream map I have made. Note that the subway map below is only fictional and that not everything below is real; some subway lines and stations do exist, some are planned, however most are just entirely made up!

subway20dream20map-01

View the map up close by selecting one of the shared files below:

PDF: https://drive.google.com/open?id=0B2eAo9vQDug-cUxzaklCT1drX28

PNG: https://drive.google.com/open?id=0B2eAo9vQDug-d1M5NjFVZnFzLUk

– Royalle

Date of Post: 08.18.16

Operation: RE-LIVE

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There’s just been a lot of things that had happened here while I was away (check my blog below entitled “So, What happened?” for the full story of what had happened to my WordPress account). Many changes in the interfaces, how the profiles were set up, as well as the daily and weekly challenges (which I have decided to begin participating).

Apart from that, most probably I would be posting stuff daily (more than usual), just to catch up for the time that I have “lost” all throughout those years without my WordPress account. Like I said from my previous post, whenever I feel like writing, I have Microsoft Word with me when I was writing (if you came to ask why I didn’t just make a new WordPress account, then the answer is that this account is way too precious to be replaced; she’s irreplaceable).

So I would continue to publish blog posts (or anything extraordinary that have happened to me or anything along those lines, like a public diary per se) and any creative pieces (such as poems, fiction stories, novel excerpts, photographs, artworks, etc.)

My goal is for this WordPress account to re-live and not die out of oblivion. Again, for all the followers I have and the likes, comments thank you so much. You are all awesome!!!

– Royalle

Date of Post: 08.18.16

Red, Red Moon

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via Daily Prompt: Moon

6918730-red-moon-night
Photo Source: 7-themes.com

“Come, look!” she cried as she came rushing through me that night while I was reviewing my notes. I didn’t even know what the hell was going on, but to my expense, alright.

She was actually referring to the beautiful sight outside the window view.

“It’s just a moon, my dear. What’s all the excitement about?” I told her as I felt the loss of excitement once I came near the window pane.

Little did she know that I felt more excited than ever, more excited than her, for seeing such a marvelous sight. That round thing in the night sky. It was a full moon. And it had the most unusual color, a color that I have never seen. Red.

But that feeling of excitement lasted only for a couple of seconds. I cherished every moment of it. It was the only thing I had that time… until I came to a full realization, that the “she” that had dragged me all the way to the window never even came to exist in the first place. It was as if she turned into air and dust upon seeing the marvelous moon. She was nothing more but a figment of my imagination.

Upon realization, tears began rolling down my face. That was one cruel night…

Moon

– Royalle

Date of Post: 08.18.16